According to the present practice of producing a hot rolled steel strip by a continuous hot rolling mill, a steel ingot which is produced by the ingot process, including slabbing, or by a continuous casting process, is used as the starting material. The thus obtained steel slab is cooled down to ambient temperature. Thereafter, this slab is heated up to a temperature in the range of 1200.degree. to 1300.degree. C over a period of more than three hours in a slab reheating furnace. It is then fed to a hot rolling mill and hot rolled into the desired thickness. The heat energy required for reheating the once-cooled steel slab to such a high temperature is tremendous.